Visibility-Graph Analysis of the Solar Wind Velocity

Abstract

We analyze in situ measurements of the solar wind velocity obtained by the Advanced Composition Explorer (ACE) and the Helios spacecraft during the years 1998 – 2012 and 1975 – 1983, respectively. The data mainly belong to solar cycles 23 (1996 – 2008) and 21 (1976 – 1986). We used the directed horizontal-visibility-graph (DHVg) algorithm and estimated a graph functional, namely, the degree distance (D), which is defined using the Kullback–Leibler divergence (KLD) to understand the time irreversibility of solar wind time-series. We estimated this degree-distance irreversibility parameter for these time-series at different phases of the solar activity cycle. The irreversibility parameter was first established for known dynamical data and was then applied to solar wind velocity time-series. It is observed that irreversibility in solar wind velocity fluctuations show a similar behavior at 0.3 AU (Helios data) and 1 AU (ACE data). Moreover, the fluctuations change over the phases of the activity cycle.